Numerous studies consider the role of social, or occupational, mobility on health inequalities. A common conclusion is that social mobility constrains, rather than widens, social class health inequalities. It is argued that such 'gradient constraint' occurs because movers into higher social classes tend to have poorer health than those they join, while movers into lower social classes tend to have better health than those they join. This has led to the suggestion that increasing social mobility may be an effective policy to reduce health inequalities. However, this raises a paradox as many studies also show that health inequalities are widening. We compare class mobility and deprivation mobility between 1971 and 1991 with health in 1991 in England and Wales. In both cases, the health in 1991 of the 'mobile' tended to fall between that of those they left and those they joined. In comparison to the socially stable, the gradient was thus constrained. However, comparing the health in 1991 of everyone by their class/deprivation position in 1991 and 1971, the overall social class health gradient was little different, while the deprivation health gap was considerably wider in 1991. These results show that a reduction in inequalities is not a necessary consequence if the health of 'mobile' people falls between that of those they left and those they joined and this is particularly the case for deprivation mobility.